Question

1. which expression is equivalent to

\\( \frac { 2 } { 3 } x + ( - 3 ) + ( - 2 ) - \frac { 1 } { 3 } x \\)?

\\( \textcircled { a } x + 5 \\)

\\( \textcircled { b } - \frac { 1 } { 3 } x - 5 \\)

\\( \textcircled { c } \frac { 1 } { 3 } x - 1 \\)

\\( \textcircled { d } \frac { 1 } { 3 } x - 5 \\)

Explanation:

Step1: Combine like terms (x - terms)

Combine \(\frac{2}{3}x\) and \(-\frac{1}{3}x\). Using the formula \(a + b\) (where \(a=\frac{2}{3}x\) and \(b =-\frac{1}{3}x\)), we have \(\frac{2}{3}x-\frac{1}{3}x=\frac{2 - 1}{3}x=\frac{1}{3}x\).

Step2: Combine constant terms

Combine \(-3\) and \(-2\). Using the formula \(a + b\) (where \(a=-3\) and \(b=-2\)), we have \(-3+( - 2)=-(3 + 2)=-5\).

Answer:

D. \(\frac{1}{3}x-5\)